Mathematical Thinking

Mathematical Thinking: From Assessment Items to Challenging Tasks is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP). Students will be exposed to the tasks used on assessments, become more confident in solving them, and see how their problem-solving ability stacks up against students nationwide.

Mathematical Thinking includes chapters on these subjects: Number and Operations; Algebraic Thinking; Geometry and Measurement; and Data Analysis, Statistics, and Probability. Each chapter begins by explaining how its topic has been treated in the NAEP assessment and what skills its lessons are designed to build.

Each activity includes the NAEP item that inspired it, sample student responses, and the percentage of students who completed it correctly. All activities include these elements:

Learning and performance goals, and a list of relevant Common Core standards and mathematical practices
A list of materials needed-with all activity sheets and templates available for download and printing at NCTM's More4U website
A step-by-step lesson plan in Launch-Explore-Summarize format, with questions and prompts to pose to students and a range of possible responses they might give
Gearing Up and Gearing Down sections to customize and extend the lessons


With these assessment-based lessons, teachers can not only help students become more adept at reaching a correct answer on tests, but they can also help them do so by becoming better mathematical thinkers and problem solvers.